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Class org.netlib.lapack.DGEBD2

java.lang.Object
   |
   +----org.netlib.lapack.DGEBD2

public class DGEBD2

extends Object

DGEBD2 is a simplified interface to the JLAPACK routine dgebd2.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines.  Using this interface also allows you
to omit offset and leading dimension arguments.  However, because
of these conversions, these routines will be slower than the low
level ones.  Following is the description from the original Fortran
source.  Contact seymour@cs.utk.edu with any questions.

 *     ..
 *
 *  Purpose
 *  =======
 *
 *  DGEBD2 reduces a real general m by n matrix A to upper or lower
 *  bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
 *
 *  If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
 *
 *  Arguments
 *  =========
 *
 *  M       (input) INTEGER
 *          The number of rows in the matrix A.  M >= 0.
 *
 *  N       (input) INTEGER
 *          The number of columns in the matrix A.  N >= 0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the m by n general matrix to be reduced.
 *          On exit,
 *          if m >= n, the diagonal and the first superdiagonal are
 *            overwritten with the upper bidiagonal matrix B; the
 *            elements below the diagonal, with the array TAUQ, represent
 *            the orthogonal matrix Q as a product of elementary
 *            reflectors, and the elements above the first superdiagonal,
 *            with the array TAUP, represent the orthogonal matrix P as
 *            a product of elementary reflectors;
 *          if m < n, the diagonal and the first subdiagonal are
 *            overwritten with the lower bidiagonal matrix B; the
 *            elements below the first subdiagonal, with the array TAUQ,
 *            represent the orthogonal matrix Q as a product of
 *            elementary reflectors, and the elements above the diagonal,
 *            with the array TAUP, represent the orthogonal matrix P as
 *            a product of elementary reflectors.
 *          See Further Details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
 *
 *  D       (output) DOUBLE PRECISION array, dimension (min(M,N))
 *          The diagonal elements of the bidiagonal matrix B:
 *          D(i) = A(i,i).
 *
 *  E       (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
 *          The off-diagonal elements of the bidiagonal matrix B:
 *          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
 *          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
 *
 *  TAUQ    (output) DOUBLE PRECISION array dimension (min(M,N))
 *          The scalar factors of the elementary reflectors which
 *          represent the orthogonal matrix Q. See Further Details.
 *
 *  TAUP    (output) DOUBLE PRECISION array, dimension (min(M,N))
 *          The scalar factors of the elementary reflectors which
 *          represent the orthogonal matrix P. See Further Details.
 *
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (max(M,N))
 *
 *  INFO    (output) INTEGER
 *          = 0: successful exit.
 *          < 0: if INFO = -i, the i-th argument had an illegal value.
 *
 *  Further Details
 *  ===============
 *
 *  The matrices Q and P are represented as products of elementary
 *  reflectors:
 *
 *  If m >= n,
 *
 *     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
 *
 *  Each H(i) and G(i) has the form:
 *
 *     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
 *  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
 *  tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  If m < n,
 *
 *     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
 *
 *  Each H(i) and G(i) has the form:
 *
 *     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
 *  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
 *  tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  The contents of A on exit are illustrated by the following examples:
 *
 *  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
 *
 *    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
 *    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
 *    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
 *    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
 *    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
 *    (  v1  v2  v3  v4  v5 )
 *
 *  where d and e denote diagonal and off-diagonal elements of B, vi
 *  denotes an element of the vector defining H(i), and ui an element of
 *  the vector defining G(i).
 *
 *  =====================================================================
 *
 *     .. Parameters ..

DGEBD2()

DGEBD2(int, int, double[][], double[], double[], double[], double[], double[], intW)

 public DGEBD2()

 public static void DGEBD2(int m,
                           int n,
                           double a[][],
                           double d[],
                           double e[],
                           double tauq[],
                           double taup[],
                           double work[],
                           intW info)

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